Blueprints are currently stored locally in a single set, which can be found here:

Each blueprint is stored in 2 files, a ‘.BP’ which contains the block data and a ‘.thumbnail’ which contains the image seen in-game. Existing blueprints will be converted into a new format when you first enter a save file. This new format uses a unique ID to identify each unique blueprint (so if you use the same blueprint 5 times in your set, they’ll share the same ID).

To share these 2 files with another user you can simply upload/send them as you would an image and have that user place them in the BlueprintSet000 folder.

These blueprints are then referenced in the BlueprintSet.json file in the same directory. After the line "blueprints": is a collection of unique IDs present in the set. Simply add these new IDs to this section.